US11454177B2 - Method of aero-engine on-line optimization and multivariable control based on model prediction - Google Patents

Method of aero-engine on-line optimization and multivariable control based on model prediction Download PDF

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US11454177B2
US11454177B2 US16/462,519 US201816462519A US11454177B2 US 11454177 B2 US11454177 B2 US 11454177B2 US 201816462519 A US201816462519 A US 201816462519A US 11454177 B2 US11454177 B2 US 11454177B2
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engine
aero
control
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US20190383221A1 (en
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Xian DU
Yanhua Ma
Ximing Sun
Zhimin Wang
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Dalian University of Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02C—GAS-TURBINE PLANTS; AIR INTAKES FOR JET-PROPULSION PLANTS; CONTROLLING FUEL SUPPLY IN AIR-BREATHING JET-PROPULSION PLANTS
    • F02C9/00—Controlling gas-turbine plants; Controlling fuel supply in air- breathing jet-propulsion plants
    • F02C9/26—Control of fuel supply
    • F02C9/28—Regulating systems responsive to plant or ambient parameters, e.g. temperature, pressure, rotor speed
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64D—EQUIPMENT FOR FITTING IN OR TO AIRCRAFT; FLIGHT SUITS; PARACHUTES; ARRANGEMENT OR MOUNTING OF POWER PLANTS OR PROPULSION TRANSMISSIONS IN AIRCRAFT
    • B64D31/00—Power plant control systems; Arrangement of power plant control systems in aircraft
    • B64D31/02—Initiating means
    • B64D31/06—Initiating means actuated automatically
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B17/00—Systems involving the use of models or simulators of said systems
    • G05B17/02—Systems involving the use of models or simulators of said systems electric
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2220/00—Application
    • F05D2220/30—Application in turbines
    • F05D2220/32—Application in turbines in gas turbines
    • F05D2220/323—Application in turbines in gas turbines for aircraft propulsion, e.g. jet engines
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2260/00—Function
    • F05D2260/80—Diagnostics
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2260/00—Function
    • F05D2260/81—Modelling or simulation
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2270/00—Control
    • F05D2270/01—Purpose of the control system
    • F05D2270/20—Purpose of the control system to optimize the performance of a machine
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
    • F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
    • F05D2270/00—Control
    • F05D2270/40—Type of control system
    • F05D2270/44—Type of control system active, predictive, or anticipative
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling

Definitions

  • the present invention provides a design method of aero-engine on-line optimization and multivariable control based on model prediction, and belongs to the technical field of control and simulation of aerospace propulsion systems.
  • Model prediction control as a model-based multivariable control algorithm not only can realize multivariable effective control for the aero-engine system, but also can treat various constraint problems to be treated in the aero-engine control process, so as to give full play to the potential of the aero-engine and improve the performance of the entire aerospace propulsion system.
  • model prediction control has multiple excellent properties, it has the defect that it is difficult to consider controller performance and real-time performance of the control system.
  • a linear model of the engine is continuously established in each control cycle, and a multivariable model predictive controller is designed on the basis of considering an actuator of the control system, thereby realizing real-time on-line optimization and improving the performance of the control system while reducing the calculation of the model prediction control.
  • the present invention proposes a design method of aero-engine on-line optimization and multivariable control based on model prediction.
  • a design method of aero-engine on-line optimization and multivariable control based on model prediction a control system structure mainly consisting of two parts: the first part is a prediction model acquisition layer that continuously establishes a small deviation linear model of an aero-engine near different steady state points based on the actual operating state of the aero-engine in each control cycle and external environment parameters and that supplies model parameters to a controller; and the second part is a control law optimizing and decision-making layer that consists of a model prediction controller and an external output feedback and determines the control output of the controller by solving a linear optimization problem with constraint and closed-loop feedback effect.
  • the specific steps are as follows:
  • step S2 normalizing the small deviation linear model of the aero-engine obtained in step S1, i.e., converting absolute increments of an input variable, a state variable and an output variable into relative increments about the steady state points through linear transformation; discretizing the normalized model so that the model parameters are convenient for use in digital control; a sampling cycle of discretization being the same as the control cycle;
  • step S4 applying the controller output obtained in step S3 to a controlled system and comparing with the actual output of the aero-engine obtained by a sensor to obtain a control error as the input of the model prediction controller; and guiding the controller to make a decision on the controller output of the next step.
  • the step of establishing a small deviation linear model of an aero-engine taking the actual input of the aero-engine and the external environment as steady state points is as follows:
  • n is a vector formed by the rotational speed of each rotor of the aero-engine
  • u in is a vector formed by the control quantity
  • u out is a vector formed by an external environment variable to be considered
  • ⁇ ⁇ M Jac [ ⁇ ⁇ n ⁇ ⁇ u i ⁇ n ]
  • Jac is a Jacobian matrix of Mf with respect to n and u in
  • ⁇ n and ⁇ u in are column vectors
  • the element of ⁇ n is the absolute increment of the rotational speed of each rotor relative to the rotational speed of the steady state point
  • the element of ⁇ u in is the absolute increment of each control quantity relative to the control quantity of the steady state point
  • n . A ⁇ ⁇ ⁇ n + B ⁇ ⁇ ⁇ u in
  • ⁇ y is a column vector, and the element thereof is an absolute increment of each aero-engine parameter other than the rotational speed relative to the steady state point;
  • the step of conducting normalization and discretization on the obtained small deviation linear model of the aero-engine is as follows:
  • subscript S indicates a vector after nondimensionalization
  • the subscript in indicates the state quantity, the input quantity and the output quantity of the aero-engine on the steady state points
  • a a is a diagonal matrix formed by a time constant negative derivative of the actuator
  • B a is a diagonal matrix formed by a time constant derivative of the actuator, and can be discretized in accordance with the same sampling time as the control cycle as follows:
  • a ad and B ad are respectively a system matrix and an input matrix after discretization of the state space expressions of the actuator
  • a t [ A ad 0 B ed ⁇ C ad A ed ]
  • B t [ B ad 0 ]
  • C t [ D ed ⁇ C ad , C ed ] ;
  • the state vector and the input vector are composed into a new augmented state vector, and the increment of the input vector is used as a new input vector to obtain augmented state space expressions:
  • a predictive field is set as p and a control field is set as q to obtain a general form of a prediction formula of a state sequence and an output sequence as follows:
  • C c [ I 0 0 ... I I 0 ... ... ... ... I I I ... ]
  • L [ I I ⁇ I ]
  • ⁇ and U are respectively an input quantity upper limit and an input matrix lower limit
  • on-line rolling optimization can be realized by solving a quadratic programming problem; and a header element of the control quantity increment sequence obtained by optimization, and the control quantity of the previous control cycle are summed to use the sum as an actual control quantity within the next control cycle.
  • the present invention proposes a design method of aero-engine on-line optimization and multivariable control based on model prediction.
  • the traditional interpolation method or fitting method is not adopted for acquisition of the prediction model.
  • a steady state model under the current state input condition is acquired in real time as an important component part of a current prediction model through the method of power extracting according to the existing nonlinear component-level model of the aero-engine.
  • the design method is closer to the actual characteristic graph of the engine compared with the traditional interpolation method and the fitting method, and can greatly reduce the calculation time and improve the real-time performance of on-line optimization compared with a solution of solving the nonlinear optimization problem by directly using the nonlinear model of the engine.
  • the present invention notes the necessity of normalization of the linear mode of the engine and considers the influence of the dynamic performance of the actuator on the control system in the process of constructing the prediction model.
  • the input vector, the output vector and the state vector have different units, and the orders of magnitude of some elements in the vectors are quite different, thereby causing great differences in the orders of magnitude of matrix elements and even generating an ill-conditioned matrix which may affect the accuracy of further calculation.
  • the present invention introduces the normalization link in the process of generating the linear model to improve the operation accuracy.
  • the time constant of the actuator is often less than the time constant of the aero-engine, for the model-based control algorithm, the introduction of the actuator still influences the control effect of the control system.
  • the actuator and the engine as two systems connected in series are combined into a whole, which achieves a better control effect in spite of increasing the orders of the systems.
  • the multivariate control system structure of the aero-engine based on model prediction designed by the present invention has a large closed loop for actual engine output, and can reflect the real response of the engine to the controller output so as to adjust the expected instruction of the model predictive controller, compensate the influence of model mismatch and external disturbance on the system and improve the control accuracy of the control system.
  • FIG. 1 is a change curve of rotational speed of a high-pressure rotor.
  • FIG. 2 is a change curve of exit pressure ratio of a turbine.
  • FIG. 3 is a change curve of temperature before turbine.
  • FIG. 4 is a change curve of fuel flow.
  • FIG. 5 is a change curve of a sectional area of a nozzle.
  • FIG. 6 is a change curve of fan surge margin.
  • FIG. 7 is a change curve of compressor surge margin.
  • FIG. 8 is a change curve of engine thrust.
  • FIG. 9 is a contrast curve of rotational speed of a high-pressure rotor under different working conditions.
  • FIG. 10 is a contrast curve of exit pressure ratio of a turbine under different working conditions.
  • FIG. 12 is a contrast curve of fuel flow under different working conditions.
  • FIG. 13 is a contrast curve of sectional area of a nozzle under different working conditions.
  • FIG. 14 is a contrast curve of fan surge margin under different working conditions.
  • FIG. 15 is a change curve of compressor surge margin under different working conditions.
  • FIG. 16 is a contrast curve of engine thrust under different working conditions.
  • FIG. 17 is a structural diagram of an aero-engine on-line optimization and multivariable control system based on model prediction.
  • the present embodiment relates to a design method of aero-engine on-line optimization and multivariable controller based on model prediction. Specific detailed design steps are as follows:
  • Step 1 establishing a small deviation linear model of an aero-engine taking the current actual input of the aero-engine and the external environment parameters as steady state points; and firstly obtaining the steady state points for calculating a small deviation linear model.
  • the small deviation model at the current time is calculated by approximately taking the input quantity at the previous sampling moment of the engine and the environmental parameters as the steady state points. The method for calculating the small deviation model of the engine near the steady state points is described below.
  • the thermal inertia of components is much smaller than the inertia of the rotor. Therefore, the heat transfer process is ignored in modeling and the engine rotor is taken as an energy storage component.
  • the engine in the embodiment is a typical two-rotor engine. Therefore, the dynamic performance of the engine depends on the torque balance equation of two rotors, i.e.:
  • J H and J L are respectively the rotational inertia of a high-pressure rotor and a low-pressure rotor of the engine; ⁇ M H and ⁇ M L are respectively the remaining torques of the high-pressure rotor and the low-pressure rotor.
  • the remaining torques of the high-pressure rotor and the low-pressure rotor can be expressed as:
  • M TH and M TL are respectively the torques of a high-pressure turbine and a low-pressure turbine
  • M CH and M CL are respectively the torques of a high-pressure compressor and a low-pressure compressor.
  • M fr,H and M fr,L are respectively friction torques of the high-pressure rotor and the low-pressure rotor. Since the values are much smaller than the other four terms, the values are ignored in the process of calculating the linear model. It is known from formula (2) that ⁇ M H and ⁇ M L are respectively the rotational speed of the high-pressure rotor and the low-pressure rotor, and are nonlinear functions of main fuel flow, the sectional area of the nozzle and the pressure and temperature of the working environment. Therefore, the formula (2) can be expanded according to Taylor formula into the following linear form:
  • ⁇ n H , ⁇ n L , ⁇ q mf , ⁇ A 8 , ⁇ p 2 and ⁇ T 2 are respectively absolute increments of variables relative to the steady state points.
  • the motion equations of the high-pressure rotor and the low-pressure rotor can be obtained as follows:
  • ⁇ ⁇ x ( ⁇ x ⁇ n H ) 0 ⁇ ⁇ ⁇ n H + ( ⁇ x ⁇ n L ) 0 ⁇ ⁇ ⁇ n L + ( ⁇ x ⁇ q m , f ) 0 ⁇ ⁇ ⁇ q mf + ( ⁇ x ⁇ A 8 ) 0 ⁇ ⁇ ⁇ A 8 ( 11 )
  • the present invention constructs a linear model of the engine through a linear state space expression.
  • the state vector is composed of two elements when only two independent rotor components are considered as energy storage elements.
  • the present invention selects the rotational speed ⁇ n H and ⁇ n L of two rotors of the two-rotor engine as state variables, and the state equation can be expressed as:
  • the adopted method for acquiring the partial derivatives of the steady state points is to extract the power of the high-pressure rotor and the low-pressure rotor of the engine based on the nonlinear calculation procedure of the engine, change the fuel flow and the sectional area of the nozzle, acquire the rotational speed of the high-pressure rotor and the low-pressure rotor, the temperature before turbine and the change quantity of the total pressure ratio of the compressor through balancing calculation and solve the partial derivatives according to the change quantity. Balancing calculation will include the calculation of the following five states:
  • State II other conditions remain unchanged; a small amount of power is extracted on the low-pressure shaft; and the engine speed and other parameter values are calculated when a small amount of power is extracted on the low-pressure shaft, and recorded as n H1 , n L1 , T 41 and ⁇ T1 .
  • State III other conditions remain unchanged; a small amount of power is extracted on the high-pressure shaft; and the engine parameter values are calculated when the power is extracted on the high-pressure shaft and recorded as n H2 , n L2 , T 42 and ⁇ T2 .
  • State IV other conditions remain unchanged; and when there is a small change in fuel flow relative to the state, the engine parameter values n H3 , n L3 , T 43 and ⁇ T3 are calculated when the fuel flow deviates from the steady state value.
  • State V other conditions remain unchanged; and when there is a small change in the sectional area of the nozzle relative to the state, the engine parameter values n H4 , n L4 , T 44 and ⁇ T4 are calculated when the sectional area of the nozzle deviates from the steady state value.
  • the undetermined partial derivatives are solved through programming by elimination with maximal column pivoting to complete the linearization of the model near the aero-engine steady state operation point.
  • Step 2 normalizing and discretizing the small deviation linear model of the aero-engine obtained in step 1.
  • Various elements in the input vector, the output vector and even the state vector use different units, and the orders of magnitude of different variables are quite different, thereby causing great differences in the orders of magnitude of the elements in the parameter matrix of the linear model of the engine, easily forming an ill-conditioned matrix and extremely easily affecting the calculating accuracy. Therefore, the model needs to be normalized.
  • the elements in the input vector, the state vector and the output vector in the formulas (12) and (13) are absolute increments.
  • the orders of magnitude of the absolute increments are quite different, which is easy to cause large errors in the computational process. Therefore, the linear normalization model of the engine is obtained by converting the absolute increments into the relative increments of the steady state operation points in the present invention.
  • the absolute increments need to be nondimensionalized into relative increments, and the expressions of the relative increments are as follows:
  • x . si x . i x m ⁇ i
  • x si x i x m ⁇ i
  • u si u i u m ⁇ i
  • y si y i y m ⁇ i ( 21 )
  • ⁇ dot over (x) ⁇ i , x i , u i and y i are elements in the corresponding vectors; x mi , u mi and y mi are respectively parameter values of the steady state points; and ⁇ dot over (x) ⁇ si , x si , u si and y si , are respectively relative increments of the elements in the vectors.
  • the collated state space expression can be expressed as follows:
  • model prediction control algorithm is a computer control algorithm
  • model needs to be discretized.
  • sampling cycle of discretization shall be consistent with the control cycle of the control system.
  • General forms of the state space expressions after discretization are indicated as follows:
  • a ed , B ed , C ed and D ed are discretized parameter matrixes.
  • Step 3 designing a model prediction multivariable controller.
  • the main work of the model prediction controller includes constructing the overall prediction model and conducting linear optimization with constraints in the finite time domain according to the expected instruction of the input controller to determine the output of the next controller.
  • the actuator Since the influence of the actuator is considered in the control system designed by the present invention and the actuator is approximated as a first-order inertial link, the actuator also needs to be considered into the prediction model. Firstly, the approximate model of the actuator is written into the state space expression shown below:
  • [ x . 1 x . 2 ] [ - 1 T 1 0 0 - 1 T 2 ] [ x 1 x 2 ] + [ 1 T 1 0 0 1 T 2 ] [ u 1 u 2 ] ( 27 )
  • [ y 1 y 2 ] [ 1 0 0 1 ] [ x 1 x 2 ] ( 28 )
  • a ad and B ad are discretized parameter matrixes of the actuator.
  • the state space expressions of the actuator and the engine can be combined in series to form the prediction model of the model prediction controller as follows:
  • x t ( k + 1 ) A t ⁇ x t ( k ) + B t ⁇ u t ( k ) ( 31 )
  • y t ( k ) C t ⁇ x t ( k ) ⁇
  • x t [ x 1 , x 2 , ⁇ ⁇ n Hs , ⁇ ⁇ n Ls ] T
  • u t [ q mfs , A 8 ] T
  • y t [ ⁇ ⁇ n Hs , ⁇ ⁇ n Ls , ⁇ ⁇ T 4 ⁇ s , ⁇ ⁇ ⁇ Ts ] T
  • a t [ A ad 0 B ed ⁇ C ad A ed ]
  • B t [ B ad 0 ]
  • C t [ D ed ⁇ C ad , C ed ] .
  • the state vector and the input vector are composed into a new augmented state vector, and the increment of the input vector is used as a new input vector to obtain augmented state space expressions of the aero-engine:
  • ⁇ u(k) is an increment vector of the control quantity within the k control cycle
  • a predictive field is set as 10 and a control field is set as 3 to obtain a general form of a prediction formula of a state sequence and an output sequence as follows:
  • x ⁇ P xx ⁇ x t ′ ( k ) + H x ⁇ u ⁇ ( 37 )
  • y ⁇ Px t ′ ( k ) + H ⁇ u ⁇ ( 38 )
  • x ⁇ [ x t ′ ⁇ T ( k + 1 )
  • x t ′ ⁇ T ( k + 2 ) ...
  • u ⁇ [ ⁇ ⁇ u T ( k ) , ⁇ ⁇ u T ( k + 1 ) , ... , ⁇ ⁇ u T ( k + 9 )
  • y ⁇ [ y t ′ ⁇ T ( k + 1 ) , y t ′ ⁇ T ( k + 2 ) , ... , y t ′ ⁇ T ( k +
  • J [ r ⁇ Px t ′( k ) ⁇ Hû ] T [ r ⁇ Px t ′( k ) ⁇ Hû ] ⁇ û T û (44)
  • r is a controller input of a reference sequence
  • J û T [ H T H+ ⁇ I ] û+ 2[ x t ′T P T H ⁇ r T H ] û (45)
  • An input constraint can be expressed as the following compact form: C c û ⁇ L ( ⁇ u ( k ⁇ 1)) (46) ⁇ C c û ⁇ L ( U ⁇ u ( k ⁇ 1)) (47) where,
  • C c [ I 0 0 L I I 0 L L L L L I I I L ]
  • L [ I I M I ]
  • ⁇ and U are respectively an input matrix upper limit and an input matrix lower limit.
  • An output matrix constraint can be expressed as the following form:
  • Y and Y are respectively output matrix upper limit and lower limit.
  • rolling optimization can be realized by solving a quadratic programming problem. After a control output increment sequence optimized is obtained, a header element of the sequence is taken as the actual control output within the next control cycle.
  • Step 4 applying the controller output obtained in step 3 to a controlled system and comparing the actual output of the aero-engine obtained by a sensor with an expected value to obtain a control error.
  • the control error will be taken as a new reference sequence in the optimization process of the model prediction controller, will affect the form of the model prediction target function and will compensate for the influence of mismatching of the prediction model and external disturbance on the control performance, so as to ensure the stability and control accuracy of the control system.
  • the output quantity of the engine related to the constraint conditions will be directly fed back to the model prediction controller so that the upper limit and the lower limit of the output variable matrix can be adjusted reasonably, to ensure that the engine input and output are not over the limit and ensure the stable and safe operation of the system.
  • the validity of the method in the present invention is verified through a set of simulation experiments in which the engine is accelerated from the beginning and the afterburner is turned on and turned off until the deceleration process is entered.
  • the simulation operation time is 70 s.
  • the rotational speed of the high-pressure rotor of the engine and the exit pressure ratio of the turbine as the controlled variables, under the conditions of altitude of 0 km and flight speed of 0Ma, the temperatures before turbine of 1650K and 1700K are taken as engine safety constraint conditions respectively.
  • the control signals applied to the control actuator are required to meet the physical constraint conditions of changing amplitude and changing rate.
  • the rotational speed of the high-pressure rotor is kept as 11622 r/min within 0-5 s and the exit pressure ratio of the turbine is 6. After 5 s, acceleration is started until a maximum state in which the afterburner is not turned on.
  • the rotational speed of the high-pressure rotor is 14500 r/min and the exit pressure ratio of the turbine is 11.
  • the fuel flow of the afterburner is increased to 5000 kg/h after 20 s from stabilization, and the control variables of the core engine are required to remain unchanged under the state of turning on the afterburner.
  • the afterburner is turned off at 40 s.
  • the afterburner is decelerated after 50 s from stabilization until reaching a predetermined new steady state point.
  • the rotational speed of the high-pressure rotor of the new steady state point is 12000 r/min and the exit pressure ratio of the turbine is 6.5.
  • FIGS. 1 and 2 it can be seen that the control variables and the control targets of the engine are fitted well.
  • the control variables can also be well stabilized at the set level after the engine turns on afterburner.
  • FIG. 3 it can be found that the controller can well limit the temperature before turbine to a safe range.
  • FIG. 4 and FIG. 5 it can be found that the controller can meet the requirements of amplitude limit and speed limit of the actuator. It can be found from FIG. 6 and FIG. 7 that because the controlled variables meet the constraint requirements of the actuator, the fan surge margin and the compressor surge margin of the engine meet the safety needs.
  • FIG. 8 it can be found that although there are differences in the constraint conditions, the controller is still very effective for the actual thrust control of the engine.
  • the rotational speed of the high-pressure rotor is kept as 11622 r/min within 0-5 s and the exit pressure ratio of the turbine is 7. After 5 s, acceleration is started until a maximum state in which the afterburner is not turned on. In this state, the rotational speed of the high-pressure rotor is 14500 r/min and the exit pressure ratio of the turbine is 11.
  • the fuel flow of the afterburner is increased to 5000 kg/h after 20 s from stabilization, and the control variables of the core engine are required to remain unchanged under the state of turning on the afterburner.
  • the afterburner is turned off at 40 s.
  • the afterburner is decelerated after 50 s from stabilization until reaching a predetermined new steady state point.
  • the rotational speed of the high-pressure rotor of the new steady state point is 12000 r/min and the exit pressure ratio of the turbine is 7.5.
  • FIGS. 9 and 10 it can be seen that steady state control variables and control targets of the engine under different working conditions are fitted well.
  • the dynamic process is slightly different, which is relevant to the change of the control input of the engine under different working conditions.
  • the control variables can also be well stabilized at the set level under different working conditions after the engine turns on afterburner.
  • FIG. 11 it can be found that the controller can well limit the temperature before turbine to a safe range.
  • FIGS. 12 and 13 it can be found that the control inputs of the engine are different under different working conditions, thereby causing the difference in the dynamic process in FIG. 9 and FIG. 10 . It can be found from FIG. 14 and FIG.

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